Method and apparatus with data processing

ABSTRACT

A processor-implemented data processing method includes: generating compressed data of first matrix data based on information of a distance between valid elements included in the first matrix data; fetching second matrix data based on the compressed data; and generating output matrix data based on the compressed data and the second matrix data.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of Korean Patent Application No.10-2019-0128714, filed on Oct. 16, 2019, in the Korean IntellectualProperty Office, the disclosure of which is incorporated herein in itsentirety by reference.

BACKGROUND 1. Field

The present disclosure relates to methods and apparatuses with dataprocessing.

2. Description of Related Art

Neural networks may refer to a computer scientific computationalarchitecture. Input data may be analyzed and valid information extractedby using a neural network device in various kinds of electronic systems.

When performing an arithmetic computation on input data and a weightmatrix in order to extract valid information, a typical neural networkmay not efficiently process the computation.

SUMMARY

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used as an aid in determining the scope of the claimed subjectmatter.

In one general aspect, a processor-implemented data processing methodincludes: generating compressed data of first matrix data based oninformation of a distance between valid elements included in the firstmatrix data; fetching second matrix data based on the compressed data;and generating output matrix data based on the compressed data and thesecond matrix data.

The valid elements included in the first matrix data may be elementshaving nonzero values.

The generating of the compressed data may include: generating thecompressed data so that information of a first valid element, amongelements included in a same row of the first matrix data, is included inthe compressed data; and generating the compressed data so thatinformation of a second valid element, among the elements included inthe same row of the first matrix data, is included in the compresseddata.

The first valid element may be an element having a smallest columnaddress among valid elements included in the same row.

The generating of the compressed data so that information of the firstvalid element is included in the compressed data may include allocatingelement value information and column address information of the firstvalid element to the compressed data, and the generating of thecompressed data so that information of the second valid element isincluded in the compressed data may include allocating element valueinformation of the second valid element and column distance information,indicating a column distance from the second valid element to a validelement having a smaller column address than a column address of thesecond valid element, to the compressed data.

The first valid element may be the valid element having the smallercolumn address than the second valid element.

The generating of the compressed data may include generating thecompressed data so that the row address of the first valid element isincluded in the compressed data.

The generating of the compressed data so that the row address of thefirst valid element is included in the compressed data may includeallocating row address information of the first valid element and anidentification bit indicating an end of a row including the first validelement to the compressed data.

The method may include storing the generated compressed data so that thevalid elements of the first matrix data are configured to be read inunits of rows.

The storing of the compressed data may include: partitioning thecompressed data into rows; and respectively storing pieces of thepartitioned compressed data in first regions of a plurality of banks.

The storing of the compressed data further may include copying portionsof the pieces of the partitioned compressed data stored in the firstregions and storing the portions in a second region of one of theplurality of banks.

The fetching of the second matrix data may include: obtaining rowaddress and column address information of the valid elements from thecompressed data; and fetching element value information of the secondmatrix data corresponding to the obtained row address and columnaddress.

The obtaining of the row address and column address information mayinclude: obtaining column address information of a first valid elementstored in the compressed data, and obtaining column address informationof a second valid element by summing column distance information storedin the compressed data with column distance information of a validelement having a smaller column address than a column address of thesecond valid element.

The generating of the compressed data may include performing a multiplyand accumulation (MAC) operation using the compressed data and thesecond matrix data.

The first matrix data may correspond to kernel weight data and thesecond matrix data may correspond to feature map data.

A non-transitory computer-readable storage medium may store instructionthat, when executed by one or more processors, configure the one or moreprocessors to perform the method.

In another general aspect, a data processing apparatus includes amemory; and one or more processors configured to: generate compresseddata of first matrix data based on information of a relative distancebetween valid elements included in the first matrix data; fetch an inputvector based on the compressed data; and generate output matrix databased on the compressed data and the second matrix data.

For the generating of the compressed data, the one or more processorsmay be configured to: generate the compressed data so that informationof a first valid element, among elements included in a same row of thefirst matrix data, is included in the compressed data; generate thecompressed data so that information of a second valid element, among theelements included in the same row of the first matrix data, is includedin the compressed data; and generate the compressed data so that a rowaddress of the first valid element is included in the compressed data.

The generating of the compressed data so that information of the firstvalid element is included in the compressed data may include allocatingelement value information and column address information of the firstvalid element to the compressed data, the generating of the compresseddata so that information of the second valid element is included in thecompressed data may include allocating element value information of thesecond valid element and column distance information, indicating acolumn distance from the second valid element to a valid element havinga smaller column address than a column address of the second validelement, to the compressed data, and the generating of the compresseddata so that the row address of the first valid element is included inthe compressed data may include allocating row address information ofthe first valid element and an identification bit indicating an end of arow including the first valid element to the compressed data.

The memory may be configured to store the generated compressed data sothat the valid elements of the first matrix data may be configured to beread in units of rows.

For the storing of the compressed data, the memory may be configured to:partition the compressed data into units of rows; and respectively storethe pieces of the partitioned compressed data in first regions of aplurality of banks.

For the storing of the compressed data, the memory may be configured tocopy portions of the pieces of the partitioned compressed data stored inthe first regions and store the portions in a second region of one ofthe plurality of banks.

The one or more processors may be configured to: obtain row addressesand column address information of the valid elements from the compresseddata; and fetch element value information of the second matrix datacorresponding to the obtained row address and column address.

The one or more processors may be configured to perform a multiply andaccumulation (MAC) operation using the compressed data and the inputvector.

The apparatus may include a memory storing instructions that, whenexecuted by the one or more processors, configure the one or moreprocessors to perform the generating of the compressed data of the firstmatrix data, the fetching of the second matrix data, and the generatingof the output matrix data.

The apparatus may be any one of a personal computer (PC), a serverdevice, a mobile device, a smart phone, a tablet device, an augmentedreality (AR) device, an internet-of-things (IoT) device, an autonomousvehicle, a robotics device, and a medical device, and the one or moreprocessors may be configured to perform any one of voice recognition,vision recognition, and image classification based on a result of theprocessing of the data.

Other features and aspects will be apparent from the following detaileddescription, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features, and advantages of certainembodiments of the disclosure will be more apparent from the followingdescription taken in conjunction with the accompanying drawings, inwhich:

FIG. 1 illustrates a neural network according to one or moreembodiments;

FIG. 2 illustrates a data processing apparatus according to one or moreembodiments;

FIG. 3 illustrates a method of processing data according to one or moreembodiments;

FIG. 4 illustrates a method of compressing data by a processor accordingto one or more embodiments;

FIG. 5 illustrates a method of storing compressed data by a processoraccording to one or more embodiments;

FIG. 6 illustrates a method of dividing and storing compressed data by aprocessor according to one or more embodiments;

FIG. 7 illustrates a method of storing partitioned compressed data by aprocessor according to one or more embodiments;

FIG. 8 illustrates a method of computing on output data by usingcompressed data by a processor according to one or more embodiments; and

FIG. 9 illustrates a method of computing on output data by usingcompressed data by a processor according to one or more embodiments.

DETAILED DESCRIPTION

The following detailed description is provided to assist the reader ingaining a comprehensive understanding of the methods, apparatuses,and/or systems described herein. However, various changes,modifications, and equivalents of the methods, apparatuses, and/orsystems described herein will be apparent after an understanding of thedisclosure of this application. For example, the sequences of operationsdescribed herein are merely examples, and are not limited to those setforth herein, but may be changed as will be apparent after anunderstanding of the disclosure of this application, with the exceptionof operations necessarily occurring in a certain order. Also,descriptions of features that are known in the art may be omitted forincreased clarity and conciseness.

Reference will now be made in detail to embodiments, examples of whichare illustrated in the accompanying drawings, wherein like referencenumerals refer to like elements throughout. In this regard, the one ormore embodiments may have different forms and should not be construed asbeing limited to the descriptions set forth herein. Accordingly, theembodiments are merely described below, by referring to the figures, toexplain aspects. As used herein, the term “and/or” includes any and allcombinations of one or more of the associated listed items. Expressionssuch as “at least one of,” when preceding a list of elements, modify theentire list of elements and do not modify the individual elements of thelist.

Unless otherwise defined, all terms, including technical and scientificterms, used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which this disclosure pertains and afteran understanding of the disclosure of this application. Terms, such asthose defined in commonly used dictionaries, are to be interpreted ashaving a meaning that is consistent with their meaning in the context ofthe relevant art and the disclosure of this application, and are not tobe interpreted in an idealized or overly formal sense unless expresslyso defined herein.

The terminology used herein is for describing various examples only, andis not to be used to limit the disclosure. The articles “a,” “an,” and“the” are intended to include the plural forms as well, unless thecontext clearly indicates otherwise. The terms “comprises,” “includes,”and “has” specify the presence of stated features, numbers, operations,members, elements, and/or combinations thereof, but do not preclude thepresence or addition of one or more other features, numbers, operations,members, elements, and/or combinations thereof. Also, in thespecification, the term “units” or “ . . . modules” denote units ormodules that process at least one function or operation, and may berealized by hardware or a combination of hardware and software.

Although terms such as “first,” “second,” and “third” may be used hereinto describe various members, components, regions, layers, or sections,these members, components, regions, layers, or sections are not to belimited by these terms. Rather, these terms are only used to distinguishone member, component, region, layer, or section from another member,component, region, layer, or section. Thus, a first member, component,region, layer, or section referred to in examples described herein mayalso be referred to as a second member, component, region, layer, orsection without departing from the teachings of the examples.

Reference will now be made in detail to the following embodiments,examples of which are illustrated in the accompanying drawings. Theembodiments may, however, be embodied in many different forms and shouldnot construed as being limited to the following description.

FIG. 1 illustrates a neural network (e.g., neural network 10) accordingto one or more embodiments.

Thus, as illustrated in FIG. 1, the neural network 10 may have astructure including an input layer, hidden layers, and an output layer.The neural network 10 may perform computations based on received inputdata (for example, I₁ and I₂), and may generate output data (forexample, O₁ and O₂) based on the result of the computations.

The neural network 10 may be a deep neural network (DNN) including twoor more hidden layers or an n-layers neural networks. For example, asshown in FIG. 1, the neural network 10 may be a DNN including an inputlayer (Layer 1), two hidden layers (Layer 2 and Layer 3), and an outputlayer (Layer 4). The DNN may include any combination of a fullyconnected neural network, a convolutional neural network (CNN), arecurrent neural network (RNN), a feedforward neural network (FNN), DeepBelief Networks, Restricted Boltzmann Machines, and the like, but is notlimited thereto.

The neural network 10 may be configured to perform, as non-limitingexamples, object classification, object recognition, voice recognition,and image recognition by mutually mapping input data and output data ina nonlinear relationship based on deep learning. Such deep learning isindicative of processor implemented machine learning schemes for solvingissues, such as issues related to automated image or speech recognitionfrom a big data set, as non-limiting examples. The deep learning may beimplemented by mapping of input data and the output data throughsupervised or unsupervised learning or training, such that when trainedthe resultant machine learning model, engine, or example NN mayintuitively map further input data to output data with a desiredaccuracy or reliability. Herein, it is noted that use of the term ‘may’with respect to an example or embodiment, e.g., as to what an example orembodiment may include or implement, means that at least one example orembodiment exists where such a feature is included or implemented whileall examples and embodiments are not limited thereto.

The neural network 10 may include fewer or more layers. Also, the neuralnetwork 10 may include layers of various structures different from thoseshown in FIG. 1.

Each of the layers included in the neural network 10 may include a“node”, a “processing element (PE)”, a “neuron” or, known as similarterms, a plurality of artificial neurons. While the nodes may bereferred to as “neurons” or “artificial neurons,” such reference is notintended to impart any relatedness with respect to how the neuralnetwork architecture computationally maps or thereby intuitivelyrecognizes information and how a human's neurons operate. I.e., theterms “neuron” and “artificial neuron” are merely a term of artreferring to the hardware implemented nodes of a neural network. Asshown in FIG. 1, Layer 1 may include two neurons and Layer 2 may includethree neurons, for example. However, this is only an example, and eachof the layers included in the neural network 10 may include variousnumbers of neurons.

Neurons included in different layers included in the neural network 10may be connected or linked to one other, and thus, may exchange data.For example, a neuron of a layer may receive data from neurons of aprevious layer and compute on the data, and may output the computationresult to neurons of a next layer. Additionally, in a recurrentconnection example, one neuron in a layer may receive data from itself,and/or from another neuron of the layer, from a previous time. Thenumber of the connections may correspond to the number of the neuronsincluded in the subsequent layer. For example, in adjacent fullyconnected layers, each neuron of a current layer may have a respectiveconnection to each neuron of the subsequent layer, noting that in someexamples such full connections may later be pruned or minimized duringtraining or optimization.

An output value of each of the neurons may be referred to as anactivation, or a value which results from such a predeterminedactivation function of the corresponding neuron. The activation may thusbe an output value of one neuron and an input value of neurons includedin a next layer, due to corresponding connection(s) with the next layer.Each of the neurons may determine its own activation value based onresultant activations and weights received from neurons included in theprevious layer. A weight is a parameter used to calculate activation ineach neuron, and may be a value allocated to a connection relationshipbetween neurons. Weights may be stored at synapses that connect neurons.For example, an output from a previous layer's neuron may be provided toas an input to a neuron of a next or subsequent layer through a weightedconnection between the previous layer's neuron and the neuron of thenext layer, with the weight of the weighted connection being variouslyadjusted during the training of the neural network until the neuralnetwork is trained for a desired objective. There may be additionalconnections to the neuron of the next layer, such as for providing abias connection value through a connection that may or may not beweighted and/or for providing the above example recurrent connectionwhich may be weighted. During training and implementation suchconnections and connection weights may be selectively implemented,removed, and varied to generate or obtain a resultant neural networkthat is thereby trained and that may be correspondingly implemented forthe trained objective, such as for any of the above example recognitionobjectives.

Accordingly, returning to FIG. 1, each of the neurons may be acomputational unit that outputs a resulting activation by receiving aninput (e.g., through such weighted connections), and may thereby map aninput-output. The computational unit may correspond to the activationfunction for a node. As a non-limiting example, when a is an activationfunction, w_(jk) ^(i) is a weight to a j^(th) neuron included in ani^(th) layer from a k^(th) neuron included in (i−1)^(th) layer, b_(j)^(i) is a bias of the j^(th) neuron included in the i^(th) layer, anda_(j) ^(i) is an activation of the j^(th) neuron of the i^(th) layer,the activation a_(j) ^(i) may follow Equation 1 below.

$\begin{matrix}{a_{j}^{i} = {\sigma\left( {{\sum\limits_{k}\left( {w_{jk}^{i}\mspace{14mu} X\mspace{14mu} a_{k}^{i - 1}} \right)} + b_{j}^{i}} \right)}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

As illustrated in Equation 1, the neural network computation may includea multiplication computation of multiplying an output value of a neuronof the previous layer (a_(k) ^(i-1)) and a weight of a synapse (w_(jk)^(i)), and an addition operation of adding the result values of eachmultiplication in the receiving neuron.

In a typical neural network, a large number of data sets may beexchanged between a plurality of interconnected channels, and a numberof computational processes may be performed through layers. However, inattempting to reduce the amount of computations for processing complexinput data, the typical neural network may only consider the position ortype of the calculator, and there is a technological problem in that thetypical neural network may not implement a computation method thatconsiders the sparsity characteristic of a weight matrix. However, aneural network of one or more embodiments may implement a method ofgenerating compressed data of a weight matrix and a method ofcalculating a weight matrix and input data considering the sparsitycharacteristic of the weight matrix, thereby solving such atechnological problem and providing a technological improvement byadvantageously considering the sparsity characteristic of the weightmatrix and thereby further reducing the amount of computations forprocessing input data over the typical neural network, as will bedescribed.

FIG. 2 illustrates a data processing apparatus 200 according to one ormore embodiments.

Referring to FIG. 2, the data processing apparatus 200 may include amemory 210 and a processor 220 (e.g., one or more processors). It willbe understood to one of ordinary skill in the art after an understandingof the present disclosure that other general-purpose components mayfurther be included in the data processing apparatus 200 in addition tothe components shown in FIG. 2.

The data processing apparatus 200 may be a device in which a neuralnetwork (e.g., the neural network of FIG. 1) is implemented. Forexample, the data processing apparatus 200 may be implemented as, orwith, various kinds of devices such as a personal computer (PC), aserver, a mobile device, an embedded device, etc. As a specific example,the data processing apparatus 200 may be, or be included in, a smartphone, a tablet device, an Augmented Reality (AR) device, an Internet ofThings (IoT) device, autonomous vehicles, robotics, medical devices,etc. that performs voice recognition, image recognition, imageclassification, etc. by using any one or any combination of the neuralnetwork layers and/or neural networks made up of one or more of thelayers of nodal convolutional interactions discussed herein, but is notlimited thereto. Also, the data processing apparatus 200 may be adedicated hardware accelerator (HW accelerator) mounted in theabove-described devices, and may be a HW accelerator, such as a neuralprocessing unit (NPU), a tensor processing unit (TPU), and a NeuralEngine, etc. which may be dedicated modules for driving neural networks.The use of the term “may” herein with respect to an example orembodiment (e.g., as to what an example or embodiment may include orimplement) means that at least one example or embodiment exists wheresuch a feature is included or implemented, while all examples are notlimited thereto.

The memory 210 may store various data processed in the data processingapparatus 200. For example, the memory 210 may store data processed bythe data processing apparatus 200 and data to be processed. Also, thememory 210 may store applications, drivers, etc. to be driven by thedata processing apparatus 200.

For example, the memory 210 may include random access memory (RAM), suchas dynamic random access memory (DRAM), static random access memory(SRAM), read-only memory (ROM), and electrically erasable programmableread-only memory (EEPROM), CD-ROM, Blu-ray or other optical diskstorage, hard disk drive (HDD), solid state drive (SSD), or flashmemory.

The processor 220 may control overall functions for implementing ordriving the neural network in the data processing apparatus 200. Forexample, the processor 220 may control the data processing apparatus 200by executing programs (or instructions) stored in the memory 210. In anembodiment, the processor 220 may be arranged in the memory 210 andimplemented in the form of a processing in memory (PIM).

The processor 220 may read/write data (for example, image data, featuremap data, kernel data, etc.) from the memory 210 and perform a PIMoperation using the read/write data. The PIM operation may denote acomputation operation including at least one of arithmetic operations,such as addition, multiplication, and accumulation, and logicaloperations, such as AND, OR, and XOR. In an example, when the dataprocessing apparatus 200 is used to implement a Recurrent Neural Network(RNN), the PIM operation may be a matrix vector multiplication (MV-Mul)operation.

The processor 220 may include a computation circuit to perform a PIMoperation. The computation circuit may denote hardware that performs acomputation task in the memory 210. Each computation circuit may beimplemented as an array of multiple logic gates, or may be implementedas a combination of an array of logic gates and a buffer thattemporarily stores data.

According to an embodiment, the data processing apparatus 200 mayinclude a plurality of memories 210, and the processor 220 may beprovided in each of the memories 210. In this case, the memory 210 maystore data in a bank, and the processor 220 corresponding to each memory210 may read the data from the bank to perform a computation. Inaddition, the processor 220 may again write the result of thecomputation to the corresponding bank.

When a typical processor performs a multiplication operation betweendata (for example, a multiplication operation between matrices, amultiplication operation between a matrix and a vector, and amultiplication operation between vectors, etc.), if invalid informationis included in data to be computed, the computation may be unnecessary.For example, the invalid information may be expressed as ‘0’, and whenany one of the data to be computed is 0, the multiplication computationbetween the data is output as 0, and it only increases the amount ofcomputations.

In order to solve such a problem, the typical processor may reduce anaccess frequency of a memory by using a single instruction multiple data(SIMD) MAC unit to process the operation of a partitioned region afterpartitioning DRAM dies or by disposing an accumulation operation of theMAC unit close to a DRAM bank. However, for the typical processor, toachieve the type change and location change of such MAC unit, there is atechnological problem in that a costly and time consumingdesign/configuration of such MAC unit may be required. On the contrary,the data processing apparatus 200 according to one or more embodimentsmay compress data considering a sparsity characteristic of the data tobe processed, and generate output data based on the compressed data, andthus, the data processing apparatus 200 according to one or moreembodiments may solve such a technological problem by significantlyreducing the amount of computations without requiring the costly andtime consuming design/configuration of such MAC unit.

Hereinafter, referring to FIGS. 3 through 9, examples of compressingdata considering the sparsity characteristic of the data and generatingoutput data based on the compressed data by the data processingapparatus 200 will be described.

FIG. 3 illustrates a method of processing data according to one or moreembodiments.

Referring to FIG. 3, the method of processing data may includeoperations processed in a time series by the data processing apparatus200 of FIG. 2. Accordingly, it may be seen that the descriptions givenwith respect to the data processing apparatus 200 depicted in FIG. 2 mayalso apply to the method of processing data of FIG. 3.

In operation S310, the processor 220 may generate compressed data offirst matrix data based on information representing a relative distancebetween valid elements included in the first matrix data.

The first matrix data may denote data in which element values to be usedin a multiplication operation between the data are expressed in a matrixform. The first matrix data may include at least one row. The firstmatrix may include a vector matrix. In an embodiment, the first matrixdata may be a weight matrix in which a weight, which is an element valueof a kernel (e.g., a kernel or filter to be used in a convolutionoperation), is expressed in a matrix form. Hereinafter, for convenienceof explanation, the first matrix data may be described as being a weightmatrix, but is not limited thereto.

A weight may be stored in the memory 210 in a matrix form as a parameterused to calculate activation in each neuron. Elements included in theweight matrix may respectively include weight value information andaddress information.

The weight value may denote a value allocated based on a connectionrelationship between neurons. The larger the weight value, the strongerthe connectivity between the corresponding two nodes may be, and thesmaller the weight value, the weaker the connectivity between thecorresponding two nodes may be. A weight value may have a value between0 and 10, for example, but is not limited thereto.

Address information may include row address information and columnaddress information. The address information may be used for fetching aninput vector and may be information indicating the position of a weightvalue in a weight matrix.

In an embodiment, a valid element may denote data on which a meaningfulMatrix Vector Multiplication (MV-Mul) operation may be performed. A“meaningful” MV-Mul operation may be an MV-Mul operation in which aresulting output vector is other than ‘0’. If any weight value in theweight matrix is ‘0’, the element of the corresponding output vector iszero. Accordingly, a valid element may denote an element having a weightvalue other than ‘0’. In other words, an invalid element, which ismeaningless to a matrix vector multiplication operation, may denote anelement having a weight value of ‘0’, and is “meaningless” because theelement of the corresponding output is zero.

The processor 220 may generate compressed data so that only informationof valid elements is included in the compressed data (e.g., bygenerating compressed data so that information of invalid elements isexcluded in the compressed data). In a neural network, when the weightmatrix has a high sparsity characteristic, the data processing apparatus200 according to one or more embodiments has an advantage in that theamount of computations of a matrix vector multiplication operation maybe significantly reduced.

In the present disclosure, the sparsity may denote whether data has aspace or the state of data that contains a space. Here, the term “space”may indicate an element having a value of ‘0’ is disposed betweenelements having values other than ‘0’ in a row or column direction of aweight matrix. As described above, a valid element in a weight matrixmay be represented by data that is a number other than ‘0’. Thus, dataof ‘0’ denotes meaningless information, which may also be interpreted asthat the corresponding data is blank (that is, no data).

The processor 220 may generate compressed data of a weight matrix basedon information representing a relative distance between the validelements. The relative distance may represent a column distance betweenvalid elements. For example, when a column address of a first validelement is 2 and a column address of a second valid element is 6, arelative distance between the first valid element and the second validelement may be 4. When the second valid element is compressed, theprocessor 220 may input 4 in address information of the second validelement instead of 6, which is a column address. The address informationmay be represented by an index bit. Since the processor 220 may inputcolumn distance information rather than column address information intothe compressed data, a total size of the compressed data may besignificantly reduced, thereby solving such a technological problem inan example by reducing the amount of computations for processing inputdata compared to the typical neural network.

The processor 220 may generate compressed data so that a weight value ofa valid element and column distance information from a current validelement to a previous valid element are included in the compressed data.Also, the processor 220 may generate compressed data so that a rowaddress of a valid element and an identification bit indicating the endof the row are included in the compressed data. An example of generatingcompressed data by the processor 220 will be described below withreference to FIG. 4.

After operation S310, the method may further include storing thegenerated compressed data so that the valid elements of the weightmatrix may be read in units of rows.

The processor 220 may partition the compressed data into rows and mayrespectively store the partitioned compressed data in a first region ofa plurality of banks. Since the data processing apparatus 200 accordingto one or more embodiments may be implemented in a PIM form, when piecesof compressed data are separately stored in a plurality of banks, andeach processor 220 separately computes a matrix vector multiplicationoperation, there is an advantage that a fast matrix vectormultiplication operation may be performed.

On the other hand, when the distribution of valid elements included in aweight matrix is irregular, the valid elements may be concentrated inany one bank. The processor 220 may obtain an effect of load balancingby copying a part of the compressed data and storing it in a secondregion of any one of the plurality of banks. In other words, a load maybe distributed in a balanced manner by allowing a bank that has alreadycompleted ahead a matrix vector multiplication operation of allocatedvalid elements to perform a matrix vector multiplication operationinstead of another bank, which has not completed the matrix vectormultiplication operation. An example of storing compressed data by theprocessor 220 will be described below with reference to FIGS. 5 through7.

In operation S320, the processor 220 may fetch second matrix data basedon the compressed data.

The second matrix data may denote data in which element values used in amultiplication operation between the data are expressed in a matrixform. The second matrix may include a vector matrix. In an embodiment,the second matrix data may denote feature map data (e.g., feature mapdata to be used in a convolution operation). Hereinafter, for theconvenience of explanation, the second data may be described based onthe feature map data, but is not limited thereto.

The feature map data may be input feature map data or output feature mapdata. In other words, the output feature map data in a previous layermay be input feature map data in a next layer. Accordingly, the secondmatrix data of operation S320 may be input feature map data or outputfeature map data. The second matrix data may be expressed in the form ofa column vector or a row vector.

The processor 220 may obtain row addresses and column addresses of validelements from the compressed data. In operation S310, when the processor220 generates the compressed data of the first matrix data based on theinformation representing a relative distance between the valid elements,the processor 220 may obtain a column address by summing column distanceinformation of the current valid element and column distance informationof the previous valid element. Also, the processor 220 may obtain a rowaddress of the current valid element based on an identification bit. Theprocessor 220 may fetch second matrix data corresponding to the obtainedrow address and column address.

In operation S330, the processor 220 may compute output data by usingthe compressed data and the second matrix data. In an example, theoutput data may correspond to an output of a convolution operationbetween the first matrix data corresponding to a kernel and the secondmatrix data corresponding to a feature map.

The processor 220 may compute output data by performing a MAC operationon the fetched second matrix data and valid elements. The output datamay be expressed in vector form. Each of the output vectors may besummed through an adder tree and stored in the memory 210 as outputdata. An example of performing a MAC operation by the processor 220 willbe described below with reference to FIGS. 8 through 9.

FIG. 4 illustrates a method of compressing data by a processor accordingto one or more embodiments.

FIG. 4 shows first matrix data 410 and compressed data 420. Although thefirst matrix data 410 of FIG. 4 is illustrated as a matrix having 8 rowsand 8 columns, the first matrix data 410 is not limited thereto, and thefirst matrix data 410 may have any number of rows and columns. Forexample, the first matrix data 410 may be expressed by a column vectorof one row and n columns.

Referring to FIG. 4, the first matrix data 410 may include a pluralityof valid elements E1 through E12. Each of the valid elements E1 throughE12 may have an element value other than ‘0’.

The processor 220 may generate compressed data so that information of afirst valid element among elements included in a same row of the firstmatrix data 410 is included in the compressed data 420 according to afirst rule.

As an example, the first valid element may denote the first validelement of each row. In an embodiment, the first valid element maydenote a valid element having the smallest column address among validelements included in the same row. For example, the first valid elementsin FIG. 4 may be E1, E3, E5, E6, E7, E9, and E11. In another embodiment,the first valid element may denote a valid element having the largestcolumn address among the valid elements included in the same row. Forexample, the first valid elements in FIG. 4 may be E2, E4, E5, E6, E10,and E12.

The first rule may be a rule for allocating element value informationand column address information of the first valid element to compresseddata. For example, in FIG. 4, the processor 220 may allocate w1 (whichis an element value of E1) and 2 (which is column address information)to the compressed data. The processor 220 may express the column addressinformation in the form of an index bit, and when the index bit is setto 4 bits, the processor 220 may thus express the column address of E1as 0X2.

The processor 220 may generate compressed data so that information of atleast one second valid element except for the first valid element isincluded in the compressed data according to a second rule.

The second valid element may denote remaining valid elements except forthe first valid element in each row. For example, the second validelements in FIG. 4 may be E2, E4, E8, E10, and E12.

As an example, the second rule may be a rule for allocating elementvalue information of the second valid element and column distanceinformation from the second valid element to a valid element ahead ofthe second valid element to the compressed data. For example, in FIG. 4,the processor 220 may allocate w2 (which is an element value of E2) and4 (which is information about a column distance D from E2 to E1) to thecompressed data. When an index bit is set to 4 bits, the processor 220may thus express the column address of E2 as 0X4. As the data processingapparatus 200 expresses 4 which is column distance information of thesecond valid element instead of 6 which is column address information ofthe second valid element, the size of the compressed data may besignificantly reduced over data of a typical neural network.

The processor 220 may generate compressed data so that the row addressof the first valid element is included in the compressed data accordingto a third rule.

As an example, the third rule may be a rule for allocating row addressinformation of the first valid element and an identification bitindicating the end of the row in which the first valid element isincluded to the compressed data. For example, in FIG. 4, the processor220 may allocate 0 (which is a row address of E2) and 0XF (which is anidentification bit) to compressed data. The identification bit 0XF maybe set to the maximum value of the index bit. In other words, whendecoding the compressed data, the processor 220 may allocate a maximumvalue to the index bit so that the termination of a row in which thefirst valid element is included is identified.

The processor 220 may generate the compressed data 420 in which onlyinformation of valid elements is included in the compressed data 420(e.g., in which information of invalid elements is excluded in thecompressed data 420). Accordingly, the first matrix data 410 may becompressed into the compressed data 420.

On the other hand, when the compressed data 420 is not read in units ofrows, a case in which the column address information of a valid elementand a row address may not be matched may occur when decoding thecompressed data 420. Accordingly, the processor 220 may store thecompressed data so that the valid elements of the first matrix data 410may be read in units of rows. A method of storing compressed data willbe described below with reference to FIG. 5.

FIG. 5 illustrates a method of storing compressed data by a processoraccording to one or more embodiments.

First matrix data 510 and compressed data 520 of FIG. 5 may respectivelycorrespond to the first matrix data 410 and the compressed data 420 ofFIG. 4.

Referring to FIG. 5, the processor 220 may store the compressed data 520so that the valid elements of the first matrix data 510 may be read inunits of rows.

The compressed data 520 may be stored in the memory 210 in units ofpreset chunks. In an example of a chunked storage layout, the compresseddata 520 may be stored in equal-sized chunks of a pre-defined size.According to the number of valid elements included in the row,information of the valid elements included in a plurality of rows may bestored as one chunk or the information of the valid elements included inone row may be separately stored as a plurality of chunks.

In an embodiment, when information ROW0 of valid elements of any one rowis separately stored in a first data chunk 521 and a second data chunk522, the processor 220 may allocate an additional row bit to the indexbit of the valid element having the largest column address among theinformation of the valid elements stored in the first data chunk 521. Inanother embodiment, when the information ROW0 of the valid elements ofany one row is separately stored in the first data chunk 521 and thesecond data chunk 522, the processor 220 may allocate an additional rowbit to the index bit of the valid element having the smallest columnaddress among the information of the valid elements stored in the seconddata chunk 522. This is to identify that, when decoding compressed data,information of valid elements stored in the first data chunk 521 and thesecond data chunk 522 is information of valid elements included in thesame row.

The first data chunk 521 may denote a data chunk including informationof a valid element having the smallest column address among validelements included in the same row. Also, the second data chunk 522 maydenote a data chunk including remaining valid elements except forinformation of valid elements stored in the first data chunk 521.

When decoding the compressed data, the processor 220 may continuouslyread the second data chunk 522 after reading the first data chunk 521.Accordingly, the processor 220 may obtain row addresses and columnaddresses of valid elements.

On the other hand, when the data processing apparatus 200 is implementedin the form of PIM, the method of storing compressed data in units ofrows described above allows a bank that has completed ahead a matrixvector multiplication operation of allocated valid elements to perform amatrix vector multiplication operation instead of another bank, whichhas not completed the matrix vector multiplication operation, and thus,it is possible to derive a load balancing effect. Hereinafter, a methodof storing compressed data for load balancing will be further describedwith reference to FIGS. 6 and 7.

FIG. 6 illustrates a method of partitioning and storing compressed databy a processor according to one or more embodiments.

Referring to FIG. 6, in operation S610, the processor 220 may partitioncompressed data in units of rows. Partitioning the compressed data intorows may denote that information of all valid elements included in onerow is included in the partitioned compressed data.

In operation S620, the processor 220 may store the partitionedcompressed data in a first region of a plurality of banks, respectively.

In operation S630, the processor 220 may copy a part of the partitionedcompressed data and store the copied compressed data in a second regionof one of the plurality of banks.

When a multiplication operation of the compressed data stored in thefirst region and second matrix data is completed, the processor 220 mayinitiate a multiplication operation of the compressed data stored in thesecond region and the first matrix data. A load of each processor 220may be balanced as any one processor 220, which has completed themultiplication operation of the allocated valid elements ahead performsthe multiplication operation of another processor 220, which has notcompleted the multiplication operation. A method of storing compresseddata for load balancing of the processors 220 will be further describedbelow with reference to FIG. 7.

FIG. 7 illustrates a method of storing partitioned compressed data by aprocessor according to one or more embodiments.

In FIG. 7, although four banks are shown, the number of banks may beless or more than four in some embodiments.

Referring to FIG. 7, the processor 220 may partition compressed data inunits of rows. The partitioned compressed data may include informationof all valid elements included in at least one row.

The processor 220 may store partitioned compressed data in a pluralityof banks. For example, the processor 220 may store partitioned firstcompressed data 811 in a first bank 810, store partitioned secondcompressed data 821 in a second bank 820, store partitioned thirdcompressed data 831 in a third bank 830, and store partitioned fourthcompressed data 841 in a fourth bank 840. The partitioned first throughfourth compressed data 811, 821, 831, and 841 may be stored in a firstregion 910 of each of the first through fourth banks 810, 820, 830, and840.

The processor 220 may copy a part of the partitioned compressed data andstore the copied compressed data in a second region of one of the firstthrough fourth banks 810, 820, 830, and 840. For example, the processor220 may copy a portion 821 a of the partitioned second compressed data821 and store it in a second region 920 of the first bank 810. Also, theprocessor 220 may copy a portion 831 a of the partitioned thirdcompressed data 831 and a portion 841 a of the partitioned fourthcompressed data 841 and may store them in the second region 920 of thefirst bank 810.

The compressed data stored in the second region 920 may also be storedso that information of valid elements is read in units of rows. Asdescribed above with reference to FIG. 5, when compressed data ispartitioned and stored, the processor 220 may inform that the pieces ofpartitioned compressed data are connected by allocating an additionalrow bit 860 to an index bit of one valid element.

The processor 220 may compute an output vector by using compressed dataand an input vector stored in the memory 210. A method of computing anoutput vector by the processor 220 will be further described below withreference to FIGS. 8 and 9.

FIG. 8 illustrates a method of computing on output data by usingcompressed data by a processor according to one or more embodiments.

Referring to FIG. 8, in operation S910, the processor 220 may obtain rowaddresses and column addresses of valid elements from compressed data.

When the first valid element is compressed according to the first ruledescribed with reference to FIG. 4, the processor 220 may obtain columnaddress information stored in the compressed data as a column address ofthe first valid element.

Also, since the second valid elements are compressed according to thesecond rule described with reference to FIG. 4, the processor 220 mayobtain, a sum of column distance information stored in the compresseddata and column distance information of a previous valid element ascolumn addresses of the second valid elements. For example, if columndistance information of any valid element to be computed is 4 and columndistance information of a previous valid element is 2, the processor 220may compute a sum of 2 and 4 as 6 as a column address of a validelement.

Also, since a row address is compressed according to the third ruledescribed with reference to FIG. 4, the processor 220 may obtain rowaddresses of valid elements based on the identification bit.

In operation S920, the processor 220 may fetch second matrix datacorresponding to the obtained row address and column address. Forexample, when the second matrix data is a column vector and the obtainedrow address and column address are (1, 6), the processor 220 may fetchan element value of the second matrix data corresponding to (6, 1).

In operation S930, the processor 220 may perform a multiply andaccumulation operation by using the compressed data and the secondmatrix data. In operation S920, since only element values of secondmatrix data corresponding to valid elements are fetched, the amount ofcomputations of the processor 220 may be significantly reduced.

FIG. 9 illustrates a method of computing on output data by usingcompressed data by a processor according to one or more embodiments.

Referring to FIG. 9, a global input/output sense amplifier (GIO SA) 1010may perform as a buffer for temporarily storing data 610 read from thememory 210. According to an embodiment, the GIO SA 1010 may beconfigured to store 256 bits of data corresponding to at least one row,and the GIO SA 1010 may receive read data of 256 bits (256-bit RD data)610 from the memory 210. The 256-bit RD data 610 may be transferred to aMAC operator 1040 and used as an operand.

Meanwhile, the second matrix data which is another operand forcomputation may be input through a data input/output (Data I/O) path.The second matrix data may be stored in input vector static randomaccess memory (SRAM) 1030 and then transferred to each MAC operator1040.

Index bits may pass through an index decoder 1020 and may be transferredto the input vector SRAM 1030. In the case of the second valid element,the index decoder 1020 may compute a column address of a correspondingvalid element by summing a column distance information stored in anindex bit with column distance information of a previous valid elementand may output a computed column address.

The input vector SRAM 1030 may fetch second matrix data based on the rowaddress and the column address received from the index decoder 1020, andthe fetched second matrix data may be input to the MAC operator 1040.

Each MAC operator 1040 may perform a computation on the compressed dataand the second matrix data transmitted from the input vector SRAM 1030and may output the result of the computation. The results of thecomputation output from each MAC operator 1040 may be summed up throughan adder tree 1050, and an output vector corresponding to a finalcomputation result may be stored in output vector SRAM 1060. An outputvector stored in the output vector SRAM 1060 may be output to theoutside through the Data I/O, and may be re-used for computation throughthe input vector SRAM 1030.

The data processing apparatuses, memories, processors, GIO SAs, indexdecoders, SRAMs, MAC operators, adder trees, data processing apparatus200, memory 210, processor 220, GIO SA 1010, index decoder 1020, SRAM1030, MAC operator 1040, adder tree 1050, SRAM 1060, and otherapparatuses, units, modules, devices, and other components describedherein with respect to FIGS. 1-9 are implemented by or representative ofhardware components. Examples of hardware components that may be used toperform the operations described in this application where appropriateinclude controllers, sensors, generators, drivers, memories,comparators, arithmetic logic modules, adders, subtractors, multipliers,dividers, integrators, and any other electronic components configured toperform the operations described in this application. In other examples,one or more of the hardware components that perform the operationsdescribed in this application are implemented by computing hardware, forexample, by one or more processors or computers. A processor or computermay be implemented by one or more processing elements, such as an arrayof logic gates, a controller and an arithmetic logic module, a digitalsignal processor, a microcomputer, a programmable logic controller, afield-programmable gate array, a programmable logic array, amicroprocessor, or any other device or combination of devices that isconfigured to respond to and execute instructions in a defined manner toachieve a desired result. In one example, a processor or computerincludes, or is connected to, one or more memories storing instructionsor software that are executed by the processor or computer. Hardwarecomponents implemented by a processor or computer may executeinstructions or software, such as an operating system (OS) and one ormore software applications that run on the OS, to perform the operationsdescribed in this application. The hardware components may also access,manipulate, process, create, and store data in response to execution ofthe instructions or software. For simplicity, the singular term“processor” or “computer” may be used in the description of the examplesdescribed in this application, but in other examples multiple processorsor computers may be used, or a processor or computer may includemultiple processing elements, or multiple types of processing elements,or both. For example, a single hardware component or two or morehardware components may be implemented by a single processor, or two ormore processors, or a processor and a controller. One or more hardwarecomponents may be implemented by one or more processors, or a processorand a controller, and one or more other hardware components may beimplemented by one or more other processors, or another processor andanother controller. One or more processors, or a processor and acontroller, may implement a single hardware component, or two or morehardware components. A hardware component may have any one or more ofdifferent processing configurations, examples of which include a singleprocessor, independent processors, parallel processors,single-instruction single-data (SISD) multiprocessing,single-instruction multiple-data (SIMD) multiprocessing,multiple-instruction single-data (MISD) multiprocessing, andmultiple-instruction multiple-data (MIMD) multiprocessing.

The methods illustrated in FIGS. 1-9 that perform the operationsdescribed in this application are performed by computing hardware, forexample, by one or more processors or computers, implemented asdescribed above executing instructions or software to perform theoperations described in this application that are performed by themethods. For example, a single operation or two or more operations maybe performed by a single processor, or two or more processors, or aprocessor and a controller. One or more operations may be performed byone or more processors, or a processor and a controller, and one or moreother operations may be performed by one or more other processors, oranother processor and another controller. One or more processors, or aprocessor and a controller, may perform a single operation, or two ormore operations.

Instructions or software to control computing hardware, for example, oneor more processors or computers, to implement the hardware componentsand perform the methods as described above may be written as computerprograms, code segments, instructions or any combination thereof, forindividually or collectively instructing or configuring the one or moreprocessors or computers to operate as a machine or special-purposecomputer to perform the operations that are performed by the hardwarecomponents and the methods as described above. In one example, theinstructions or software include machine code that is directly executedby the one or more processors or computers, such as machine codeproduced by a compiler. In another example, the instructions or softwareincludes higher-level code that is executed by the one or moreprocessors or computer using an interpreter. The instructions orsoftware may be written using any programming language based on theblock diagrams and the flow charts illustrated in the drawings and thecorresponding descriptions used herein, which disclose algorithms forperforming the operations that are performed by the hardware componentsand the methods as described above.

The instructions or software to control computing hardware, for example,one or more processors or computers, to implement the hardwarecomponents and perform the methods as described above, and anyassociated data, data files, and data structures, may be recorded,stored, or fixed in or on one or more non-transitory computer-readablestorage media. Examples of a non-transitory computer-readable storagemedium include read-only memory (ROM), random-access programmable readonly memory (PROM), electrically erasable programmable read-only memory(EEPROM), random-access memory (RAM), dynamic random access memory(DRAM), static random access memory (SRAM), flash memory, non-volatilememory, CD-ROMs, CD-Rs, CD+Rs, CD-RWs, CD+RWs, DVD-ROMs, DVD-Rs, DVD+Rs,DVD-RWs, DVD+RWs, DVD-RAMs, BD-ROMs, BD-Rs, BD-R LTHs, BD-REs, blue-rayor optical disk storage, hard disk drive (HDD), solid state drive (SSD),flash memory, a card type memory such as multimedia card micro or a card(for example, secure digital (SD) or extreme digital (XD)), magnetictapes, floppy disks, magneto-optical data storage devices, optical datastorage devices, hard disks, solid-state disks, and any other devicethat is configured to store the instructions or software and anyassociated data, data files, and data structures in a non-transitorymanner and provide the instructions or software and any associated data,data files, and data structures to one or more processors or computersso that the one or more processors or computers can execute theinstructions. In one example, the instructions or software and anyassociated data, data files, and data structures are distributed overnetwork-coupled computer systems so that the instructions and softwareand any associated data, data files, and data structures are stored,accessed, and executed in a distributed fashion by the one or moreprocessors or computers.

While this disclosure includes specific examples, it will be apparentafter an understanding of the disclosure of this application thatvarious changes in form and details may be made in these exampleswithout departing from the spirit and scope of the claims and theirequivalents. The examples described herein are to be considered in adescriptive sense only, and not for purposes of limitation. Descriptionsof features or aspects in each example are to be considered as beingapplicable to similar features or aspects in other examples. Suitableresults may be achieved if the described techniques are performed in adifferent order, and/or if components in a described system,architecture, device, or circuit are combined in a different manner,and/or replaced or supplemented by other components or theirequivalents. Therefore, the scope of the disclosure is defined not bythe detailed description, but by the claims and their equivalents, andall variations within the scope of the claims and their equivalents areto be construed as being included in the disclosure.

What is claimed is:
 1. A processor-implemented data processing method,the method comprising: generating compressed data of first matrix databased on information of a distance between valid elements included inthe first matrix data; fetching second matrix data based on thecompressed data; and generating output matrix data based on thecompressed data and the second matrix data.
 2. The method of claim 1,wherein the generating of the compressed data comprises: generating thecompressed data so that information of a first valid element, amongelements included in a same row of the first matrix data, is included inthe compressed data; and generating the compressed data so thatinformation of a second valid element, among the elements included inthe same row of the first matrix data, is included in the compresseddata.
 3. The method of claim 2, wherein the generating of the compresseddata so that information of the first valid element is included in thecompressed data comprises allocating element value information andcolumn address information of the first valid element to the compresseddata, and the generating of the compressed data so that information ofthe second valid element is included in the compressed data comprisesallocating element value information of the second valid element andcolumn distance information, indicating a column distance from thesecond valid element to a valid element having a smaller column addressthan a column address of the second valid element, to the compresseddata.
 4. The method of claim 1, wherein the generating of the compresseddata comprises generating the compressed data so that the row address ofthe first valid element is included in the compressed data.
 5. Themethod of claim 4, wherein the generating of the compressed data so thatthe row address of the first valid element is included in the compresseddata comprises allocating row address information of the first validelement and an identification bit indicating an end of a row includingthe first valid element to the compressed data.
 6. The method of claim1, further comprising storing the generated compressed data so that thevalid elements of the first matrix data are configured to be read inunits of rows.
 7. The method of claim 6, wherein the storing of thecompressed data comprises: partitioning the compressed data into rows;and respectively storing pieces of the partitioned compressed data infirst regions of a plurality of banks.
 8. The method of claim 7, whereinthe storing of the compressed data further comprises copying portions ofthe pieces of the partitioned compressed data stored in the firstregions and storing the portions in a second region of one of theplurality of banks.
 9. The method of claim 1, wherein the fetching ofthe second matrix data comprises: obtaining row address and columnaddress information of the valid elements from the compressed data; andfetching element value information of the second matrix datacorresponding to the obtained row address and column address.
 10. Themethod of claim 9, wherein the obtaining of the row address and columnaddress information comprises: obtaining column address information of afirst valid element stored in the compressed data, and obtaining columnaddress information of a second valid element by summing column distanceinformation stored in the compressed data with column distanceinformation of a valid element having a smaller column address than acolumn address of the second valid element.
 11. The method of claim 1,wherein the generating of the compressed data comprises performing amultiply and accumulation (MAC) operation using the compressed data andthe second matrix data.
 12. A non-transitory computer-readable storagemedium storing instruction that, when executed by one or moreprocessors, configure the one or more processors to perform the methodof claim
 1. 13. A data processing apparatus comprising: a memory; andone or more processors configured to: generate compressed data of firstmatrix data based on information of a distance between valid elementsincluded in the first matrix data; fetch an input vector based on thecompressed data; and generate output matrix data based on the compresseddata and the second matrix data.
 14. The data processing apparatus ofclaim 13, wherein, for the generating of the compressed data, the one ormore processors are configured to: generate the compressed data so thatinformation of a first valid element, among elements included in a samerow of the first matrix data, is included in the compressed data;generate the compressed data so that information of a second validelement, among the elements included in the same row of the first matrixdata, is included in the compressed data; and generate the compresseddata so that a row address of the first valid element is included in thecompressed data.
 15. The data processing apparatus of claim 14, whereinthe generating of the compressed data so that information of the firstvalid element is included in the compressed data comprises allocatingelement value information and column address information of the firstvalid element to the compressed data, the generating of the compresseddata so that information of the second valid element is included in thecompressed data comprises allocating element value information of thesecond valid element and column distance information, indicating acolumn distance from the second valid element to a valid element havinga smaller column address than a column address of the second validelement, to the compressed data, and the generating of the compresseddata so that the row address of the first valid element is included inthe compressed data comprises allocating row address information of thefirst valid element and an identification bit indicating an end of a rowincluding the first valid element to the compressed data.
 16. The dataprocessing apparatus of claim 13, wherein the memory is configured tostore the generated compressed data so that the valid elements of thefirst matrix data are configured to be read in units of rows.
 17. Thedata processing apparatus of claim 16, wherein, for the storing of thecompressed data, the memory is configured to: partition the compresseddata into units of rows; and respectively store the pieces of thepartitioned compressed data in first regions of a plurality of banks.18. The data processing apparatus of claim 17, wherein, for the storingof the compressed data, the memory is configured to copy portions of thepieces of the partitioned compressed data stored in the first regionsand store the portions in a second region of one of the plurality ofbanks.
 19. The data processing apparatus of claim 13, wherein the one ormore processors are configured to: obtain row addresses and columnaddress information of the valid elements from the compressed data; andfetch element value information of the second matrix data correspondingto the obtained row address and column address.
 20. The data processingapparatus of claim 13, wherein the one or more processors are configuredto perform a multiply and accumulation (MAC) operation using thecompressed data and the input vector.